C. Kimberling defined the concept of triangle center function in order to describe centers of triangles as points associated to some functions depending on the sidelengths, instead of in terms of geometrical properties. In this article we provide two definitions of n-gon center function for \(n\ge 3\): one of them in terms of the coordinates of the vertices and the other one by means of the lengths of the sides and the diagonals. Both of them are natural ways to generalize the concept of triangle center function, and we prove that they are equivalent. Moreover, we use n-gon center functions to associate to each polygon a point in the plane, that we call center. We also explore the problem of characterization of families of polygons in terms of these n-gon center functions and we study the relation between our new definitions and other approaches arising from Applied Mathematics.

C. Kimberling定义了三角形中心函数的概念，以便将三角形的中心描述为与某些函数相关的点，这取决于边长，而不是根据几何属性。在本文中，我们为\（n \ ge 3 \）提供了n -gon中心函数的两种定义：一种是根据顶点的坐标，另一种是通过边和对角线的长度。两者都是概括三角中心函数概念的自然方法，我们证明它们是等效的。此外，我们使用n -gon中心函数将平面中的一个点（称为中心）与每个多边形相关联。我们还从这些角度探讨了表征多边形族的问题n- gon中心函数，我们研究了新定义与应用数学带来的其他方法之间的关系。